Toki et al. [1]} conduct DNSs of planar turbulent channel flows driven by a body force with a wall-normal temperature gradient. The working fluid is nitrogen at a supercritical pressure, which is approximately 1.3 times its critical pressure. Since the ideal-gas assumption becomes invalid, the Soave-Redlich-Kwong (SRK) [2]} equation of state is employed. The bottom wall (116 K) is colder than its pseudocritical temperature (131.8 K at 4.4 MPa) while the top wall is hotter. Toki et al. [1]} evaluate the thermal conductivity \(\lambda \)  and the viscosity coefficient \(\mu \)  using the formula by Chung [4]}. Two cases named R4 and R8 are considered, whose density ratio of the two walls is 4 and 8, respectively, and their corresponding temperatures at the top wall are 149 K and 219 K. The friction Reynolds number \(Re_{\tau }\)  is approximately 390 at the cold wall, 268 and 122 at the top wall for R4 and R8 respectively. The channel is \(3\pi H\)  in length and \(\pi H\)  in the spanwise direction, where \(H\)  is the half-height of the channel. The no-slip condition is applied on the top and bottom walls. Periodic boundary conditions are applied in both the spanwise and streamwise directions.
